Save reasoning_content from litellm as details

[muupan]

Resolves #927

This PR enables saving reasoning_content returned by litellm in the details file.

How I tested

I'm using vllm==0.9.2 and litellm==1.74.15.post2.

# Start vLLM server
vllm serve Qwen/Qwen3-1.7B --tensor-parallel-size 2 --trust-remote-code --dtype bfloat16 --gpu-memory-utilization 0.9 --max_model_len 32768 --reasoning-parser qwen3

# Evaluate via litellm entry point
lighteval endpoint litellm "model_name=hosted_vllm/Qwen/Qwen3-1.7B,base_url=http://0.0.0.0:8000/v1,api_key=\"\",generation_parameters={temperature:1,max_new_tokens:16000}" "lighteval|math_500|0|0" --save-details

# Check the content of the details file (only first example)
echo results/details/hosted_vllm/Qwen/Qwen3-1.7B/2025-08-19T22-27-32.231875/details_lighteval\|math_500\|0_2025-08-19T22-27-32.231875.parquet | python -c "import pandas as pd; print(pd.read_parquet(input().strip()).head(1).to_json())" | jq > reasonings_sample.json

"reasonings" is added under "model_response". Since it is too large to paste the content here, I attached the json file.
reasonings_sample.json

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